Modeling errors for an estimation process can be tackled via a supervised approach.
Consider an estimator, ICP in our case, using sensory data \(\mathbfcal {C}_i = \lbrace  \mathbfcal {P}_i, \mathbfcal {Q}_{i+1} \rbrace \)  with \(\mathbfcal {P}_i \in \mathbb {R}^{n_i}\)  and \( \mathbfcal {Q}_{i+1} \in \mathbb {R}^{n_{i+1}}\) .
Its output \(^i\hat{{\mathbf {T}}}_{i+1}\)  is an estimate of the ground truth transformation \(^i{\mathbf {T}}_{i+1}\) .
In practice, the point clouds used in the algorithm are the result of several filters [1]}.
The actual input data is a pair of decimated point clouds \(\bar{\mathbfcal {C}}_i = \lbrace  \bar{\mathbfcal {P}}_i, \bar{\mathbfcal {Q}}_{i+1} \rbrace \)  with \( \bar{\mathbfcal {P}}_i \in \mathbb {R}^{m_i}, m_i\ll n_i\)  and \( \bar{\mathbfcal {Q}}_{i+1} \in \mathbb {R}^{m_{i+1}}, m_{i+1}\ll n_{i+1}\) .
The error of ICP is computed as
\({\mathbf {e}}_i\ =\ ^i\hat{{\mathbf {T}}}^{-1}_{i+1}\ \cdot \ ^i{\mathbf {T}}_{i+1}\) 
